Possible existence of galactic wormholes in f(R,T) gravity

To identify more deliberate f(R, T) astrophysical solutions of the wormhole geometries, we proceed under the assumption of spherical symmetry solutions of the Einstein field equations under the f(R, T) theory of gravity. For the exact solutions to the field equations, it is assumed that the gravitational Lagrangian may be written as a linear function of the Ricci scalar R and the trace of the stress-energy tensor T, i.e. f(R,T)=R+2χT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(R, T )=R+2\chi T$$\end{document}, where χ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi$$\end{document}is a constant. We carefully apply different strategies to design solutions with wormhole characteristics and properties based on constraints on wormhole geometry. Wormhole solutions are obtain here for three different density, namely, Navarro–Frenk–White density profile (NFW), Universal Rotation Curve dark matter profile (URC) and mass density profile. We provide numerous examples of wormholes where the matter threading the wormhole throat satisfies all of the energy constraints and explore general procedures for finding them using a completely general approach. Depending on whether χ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi$$\end{document} is present or absent, solutions are divided into two categories, the GR branch and non-GR branch. Finally, we postulate a smooth transition to simplify the nonlinear Einstein field equations and we can see a specific exact wormhole in absence of exotic matter.